1  20
Next
Number of results to display per page
1. Modern Fourier analysis [2009]
 Grafakos, Loukas.
 2nd ed.  New York : Springer, c2009.
 Description
 Book — xv, 504 p. : ill. ; 24 cm.
 Summary

 Preface. Smoothness and Function Spaces. BMO and Carleson Measures. Singular Integrals of Nonconvolution Type. Weighted Inequalities. Boundedness and Convergence of Fourier Integrals. TimeFrequency Analysis and the CarlesonHunt Theorem. Glossary. References. Index..
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA403.5 .G736 2009  Available 
 CAMPOS, RAFAEL G.
 [S.l.] : SPRINGER NATURE, 2019.
 Description
 Book — 1 online resource
 Summary

 Intro; ANHA Series Preface; Preface; Contents; 1 Introduction; 2 The Ordinary Discrete Fourier Transform; 2.1 Some Basic Preliminaries; 2.2 Periodic Approximation to the Fourier Transform; 2.3 Some Properties of the DFT; 2.3.1 Differentiation Matrices for Trigonometric Polynomials; 2.3.2 Changing the Period; 2.3.3 Discrete Rotations; 2.3.4 Translations with the DFT; 2.3.5 TwoDimensional DFT; 2.4 Some Fun with the DFT; 2.4.1 Translations and the Möbius Band; 2.5 Applications to Elliptic Functions; 2.5.1 A Fractional Partial Differential Equation for Theta Functions
 2.5.2 Computing Jacobi Elliptic Functions3 XFT: A Discrete Fourier Transform; 3.1 Discrete Hermite Functions and Asymptotics; 3.1.1 Orthogonality Relations; 3.1.2 Parity and Orthogonality; 3.1.3 A Discrete Schrödinger's Equation; 3.2 Quadrature of the Fractional Fourier Transform; 3.3 Discrete Fourier Cosine and Sine Transforms; 3.4 Differentiation Matrices and the XFT; 3.4.1 Discrete Derivatives in L2(∞, ∞); 3.4.1.1 A Quadrature Formula; 3.4.1.2 A Simple Initial Value Problem; 3.4.2 Parity and Differentiation; 3.4.2.1 The Case of N Even; 3.4.2.2 The Case of N Odd
 3.4.3 Derivatives of Functions Not Decreasing at Infinity3.4.3.1 A First Idea: Regularization; 3.4.3.2 Parity Considerations; 3.4.4 Further Properties of Differentiation Matrices; 3.5 Fast Algorithms for the XFT; 3.5.1 A Fast XFT; 3.5.1.1 The XFT Versus the DFT; 3.5.2 A Fast Discrete Cosine Transform; 3.5.2.1 Numerical Performance; 3.5.3 Fast Differentiation Matrices; 3.5.3.1 Numerical Performance; 3.5.3.2 Two Remarks on Algorithm 3.3; 3.6 Sampling and Aliasing; 3.6.1 Sampling; 3.6.1.1 XFT of Sampled Data; 3.6.1.2 Differintegral Scheme for Sampled Data; 3.6.2 Aliasing; 3.7 TwoDimensional XFT
 3.8 Partial Differentiation Matrices4 Applications of the XFT; 4.1 Having Fun with the XFT; 4.1.1 Translations in the XFT Formalism; 4.1.1.1 Two Variables; 4.1.2 Autostereograms; 4.1.3 Steganography; 4.2 Similarity of Brain Signals; 4.3 Edge Detection; 4.4 Boundary Value Problems; 4.4.1 Nonlinear Second Order Boundary Value Problems; 4.4.1.1 A Numerical Example; 4.4.2 Higher Order Boundary Value Problems; 4.4.3 A Solitary Problem; 4.5 Initial Value Problems; 4.5.1 One Variable; 4.5.1.1 OneTime Scheme; 4.5.1.2 TwoTime Scheme; 4.5.2 Examples; 4.5.2.1 The Cavity Collapse Problem
 4.5.2.2 A Stiff Problem4.5.3 Two Components; 4.5.3.1 An Example; 4.6 Nonlinear Partial Differential Equations; 4.6.1 OneTime Scheme; 4.6.2 TwoTime Scheme; 4.6.3 A KdV Equation; 4.6.4 Vector Burgers' Equation; 4.6.4.1 Numerical Example; 4.7 Fractional Differentiation/Integration; 4.7.1 Fractional Initial Value Problems; 4.7.1.1 A Nonlinear Problem; 4.7.2 Fractional Boundary Value Problems; 4.7.2.1 A Boundary Value Problem; 4.8 Inversion of Convolution Operators; 4.8.1 The Hilbert Transform; 4.8.2 A ShortTime Fourier Transform; 4.8.3 Dirac Delta Function; 4.8.4 The Laplace Transform
3. Numerical Fourier analysis [2018]
 Plonka, Gerlind, author.
 Cham, Switzerland : Birkhäuser, 2018.
 Description
 Book — 1 online resource (xvi, 618 pages) : illustrations (some color).
 Olson, Tim author.
 New York : Birkhäuser, [2017]
 Description
 Book — xvi, 302 pages ; 24 cm
 Summary

 Introduction: From Linear Algebra to Linear Analysis. Basic Fourier Series. The Discrete Fourier Transform. The Fourier Transform. Sampling and Interpolation. Digital Communications. Radar Processing. Image Processing. Medical Imaging. Partial Differential Equations.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .O47 2017  Unknown 
5. Classical Fourier analysis [2014]
 Grafakos, Loukas.
 Third edition.  New York : Springer, [2014]
 Description
 Book — xvii, 638 pages : illustrations ; 25 cm.
 Summary

 Preface.
 1. Lp Spaces and Interpolation.
 2. Maximal Functions, Fourier Transform, and Distributions.
 3. Fourier Series.
 4. Topics on Fourier Series.
 5. Singular Integrals of Convolution Type.
 6. LittlewoodPaley Theory and Multipliers.
 7. Weighted Inequalities. A. Gamma and Beta Functions. B. Bessel Functions. C. Rademacher Functions. D. Spherical Coordinates. E. Some Trigonometric Identities and Inequalities. F. Summation by Parts. G. Basic Functional Analysis. H. The Minimax Lemma. I. Taylor's and Mean Value Theorem in Several Variables. J. The Whitney Decomposition of Open Sets in Rn. Glossary. References. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .G733 2014  Unknown 
6. Modern Fourier analysis [2014]
 Grafakos, Loukas.
 Third edition.  New York : Springer, [2014]
 Description
 Book — xvi, 624 pages : illustrations ; 24 cm.
 Summary

 Preface. Smoothness and Function Spaces. BMO and Carleson Measures. Singular Integrals of Nonconvolution Type. Weighted Inequalities. Boundedness and Convergence of Fourier Integrals. TimeFrequency Analysis and the CarlesonHunt Theorem. Multilinear Harmonic Analysis. Glossary. References. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .G736 2014  Unknown 
7. Higher order Fourier analysis [2012]
 Tao, Terence, 1975
 Providence, Rhode Island : American Mathematical Society, [2012]
 Description
 Book — x, 187 pages : illustrations ; 26 cm.
 Summary

Traditional Fourier analysis, which has been remarkably effective in many contexts, uses linear phase functions to study functions. Some questions, such as problems involving arithmetic progressions, naturally lead to the use of quadratic or higher order phases. Higher order Fourier analysis is a subject that has become very active only recently. Gowers, in groundbreaking work, developed many of the basic concepts of this theory in order to give a new, quantitative proof of Szemeredi's theorem on arithmetic progressions. However, there are also precursors to this theory in Weyl's classical theory of equidistribution, as well as in Furstenberg's structural theory of dynamical systems. This book, which is the first monograph in this area, aims to cover all of these topics in a unified manner, as well as to survey some of the most recent developments, such as the application of the theory to count linear patterns in primes. The book serves as an introduction to the field, giving the beginning graduate student in the subject a highlevel overview of the field. The text focuses on the simplest illustrative examples of key results, serving as a companion to the existing literature on the subject. There are numerous exercises with which to test one's knowledge.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .T36 2012  Unknown 
8. Discrete fourier analysis [2011]
 Wong, M. W. (Man Wah), 1951
 Basel : Birkhäuser, ©2011.
 Description
 Book — 1 online resource (viii, 176 pages).
 Summary

 1. The finite fourier transform
 2. Translationinvariant linear operators
 3. Circulant matrices
 4. Convolution operators
 5. Fourier multipliers
 6. Eigenvalues and Eigenfunctions
 7. The fast fourier transform
 8. Timefrequency analysis
 9. Timefrequency localized bases
 10. Wavelet transforms and filter banks
 11. Haar wavelets
 12. Daubechies wavelets
 13. The trace
 14. Hilbert spaces
 15. Bounded linear operators
 16. Selfadjoint operators
 17. Compact operators
 18. The spectral theorem
 19. Schattevon Neumann classes
 20. Fourier series
 21. Fourier multipliers
 22. Pseudodifferential operators on S¹
 23. Pseudodifferential operators on Z.
 Marks, Robert J., II (Robert Jackson), 1950
 Oxford ; New York : Oxford University Press, 2009.
 Description
 Book — xxvi, 772 p. : ill. ; 26 cm.
 Summary

 1. Introduction
 2. Fundamentals of Fourier Analysis
 3. Fourier Analysis in Systems Theory
 4. Fourier Transforms in Probability, Random Variables and Stochastic Processes
 5. The Sampling Theory
 6. Generalizations of the Sampling Theorem
 7. Noise and Error Effects
 8. Multidimensional Signal Analysis
 9. TimeFrequency Representations
 10. Signal Recovery
 11. Signal and Image Synthesis: Alternating Projections Onto Convex Sets
 12. Mathematical Morphology and Fourier Analysis on Time Sales
 13. Applications
 14. Appendices
 15. Reference.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .M47 2009  Unknown 
10. Classical Fourier analysis [2008]
 Grafakos, Loukas.
 2nd ed.  New York : Springer, 2008.
 Description
 Book — xvi, 489 p. : ill. ; 25 cm.
 Summary

 Preface. Lp Spaces and Interpolation. Maximal Functions, Fourier Transform, and Distributions. Fourier Analysis on the Torus. Singular Integrals of Convolution Type. LittlewoodPaley Theory and Multipliers. Gamma and Beta Functions. Bessel Functions. Rademacher Functions. Spherical Coordinates. Some Trigonometric Identities and Inequalities. Summation by Parts. Basic Functional Analysis. The Minimax Lemma. The Schur Lemma. The Whitney Decomposition of Open Sets in Rn. Smoothness and Vanishing Moments. Glossary. References. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA403.5 .G733 2008  Available 
11. A first course in Fourier analysis [2007]
 Kammler, David W., 1940
 Rev. ed.  Cambridge ; New York : Cambridge University Press, c2007.
 Description
 Book — 1 v. (various pagings) : ill. ; 25 cm.
 Summary

 1. Fourier's representation for functions on R, Tp, Z, and PN
 2. Convolution of functions on R, Tp, Z and PN
 3. The calculus for finding Fourier transforms of functions of R
 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN
 5. Operator identities associated with Fourier analysis
 6. The fast Fourier transform
 7. Generalized functions on R
 8. Sampling
 9. Partial differential equations
 10. Wavelets
 11. Musical tones
 12. Probability
 Appendix 0. The impact of Fourier analysis
 Appendix 1. Functions and their Fourier transforms
 Appendix 2. The Fourier transform calculus
 Appendix 3. Operators and their Fourier transforms
 Appendix 4. The WhittakerRobinson flow chart for harmonic analysis
 Appendix 5. FORTRAN code for a Radix 2 FFT
 Appendix 6. The standard normal probability distribution
 Appendix 7. Frequencies of the piano keyboard Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .K36 2007  Unavailable Checked out  Overdue Request 
QA403.5 .K36 2007  Unknown 
 Kammler, David W., 1940
 Rev. ed.  Cambridge ; New York : Cambridge University Press, c2007.
 Description
 Book — 1 v. (various pagings) : ill.
 Summary

 1. Fourier's representation for functions on R, Tp, Z, and PN
 2. Convolution of functions on R, Tp, Z and PN
 3. The calculus for finding Fourier transforms of functions of R
 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN
 5. Operator identities associated with Fourier analysis
 6. The fast Fourier transform
 7. Generalized functions on R
 8. Sampling
 9. Partial differential equations
 10. Wavelets
 11. Musical tones
 12. Probability
 Appendix 0. The impact of Fourier analysis
 Appendix 1. Functions and their Fourier transforms
 Appendix 2. The Fourier transform calculus
 Appendix 3. Operators and their Fourier transforms
 Appendix 4. The WhittakerRobinson flow chart for harmonic analysis
 Appendix 5. FORTRAN code for a Radix 2 FFT
 Appendix 6. The standard normal probability distribution
 Appendix 7. Frequencies of the piano keyboard Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
13. Fourier analysis [2005]
 Stade, Eric, 1961
 Hoboken, N.J. : WileyInterscience, c2005.
 Description
 Book — xxiv, 488 p. : ill. 25 cm.
 Summary

 Preface.Introduction.1. Fourier Coefficients and Fourier Series.2. Fourier Series and Boundary Value Problems.3. L2 Spaces: Optimal Contexts for Fourier Series.4. SturmLiouville Problems.5. A Splat and a Spike.6. Fourier Transforms and Fourier Integrals.7. Special Topics and Applications.8. Local Frequency Analysis and Wavelets.Appendix.References.Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .S73 2005  Unknown 
14. Classical and modern Fourier analysis [2004]
 Grafakos, Loukas.
 Upper Saddle River, N.J. : Pearson/Prentice Hall, c2004.
 Description
 Book — xii, 859, 72 p. : ill. ; 25 cm.
 Summary

 Prolegomena.
 1. L p Spaces and Interpolation.
 2. Maximal Functions, Fourier Transform, and Distributions.
 3. Fourier Analysis on the Torus.
 4. Singular Integrals of Convolution Type.
 5. LittlewoodPaley Theory and Multipliers.
 6. Smoothness and Function Spaces.
 7. BMO and Carleson Measures.
 8. Singular Integrals of Nonconvolution Type.
 9. Weighted Inequalities.
 10. Boundedness and Convergence of Fourier Integrals. Bibliography. Index of Notation. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .G73 2004  Unknown 
15. Fourier analysis and its applications [2003]
 Vretblad, Anders.
 New York : Springer, c2003.
 Description
 Book — xi, 269 p. : ill. ; 25 cm.
 Summary

 Introduction * Preparations * Laplace and Z Transforms * Fourier Series * L^2 Theory * Separation of Variables * Fourier Transforms * Distributions * MultiDimentional Fourier Analysis * Appendix A: The ubiquitous convolution * Appendix B: The Discrete Fourier Transform * Appendix C: Formulae * Appendix D: Answers to exercises * Appendix E: Literature.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .V74 2003  Unknown 
16. Fourier analysis [2001]
 Análisis de Fourier. English
 Duoandikoetxea Zuazo, Javier.
 Providence, R.I. : American Mathematical Society, c2001.
 Description
 Book — xviii, 222 p. ; 27 cm.
 Summary

 Fourier series and integrals The HardyLittlewood maximal function The Hilbert transform Singular integrals (I) Singular integrals (II) $H^1$ and $BMO$ Weighted inequalities LittlewoodPaley theory and multipliers The $T1$ theorem Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .D8313 2001  Unknown 
 Wei, Y. (Yuchuan), 1966
 Boston : Kluwer Academic Publishers, c2000.
 Description
 Book — xi, 156 p. : ill. ; 24 cm.
 Summary

 1. ABC of Number Theory.
 2. Square Wave Analysis.
 3. Triangular Wave Analysis and Trapezoidal Wave Analysis.
 4. Frequency Analysis Based on General Periodic Functions.
 5. Main Relations and Basic Techniques.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online

Available by special arrangement in response to the COVID19 outbreak. Simultaneous access is limited.
More about HathiTrust ETAS
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA403.5 .W45 2000  Available 
 Gasquet, Claude.
 New York : Springer, c1999.
 Description
 Book — xviii, 442 p. : ill. ; 24 cm.
 Summary

 Signals and Systems. Periodic Signals. The Discrete Fourier Transform and Numerical Computations. The Lebesgue Integral. Spaces. Convolution and the Fourier Transform of Functions. Analog Filters. Distributions. Convolution and the Fourier Transform of Distributions. Filters and Distributions. Sampling and Discrete Filters. Current Trends: TimeFrequency Analysis. References.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA403.5 .G37 1999  Unknown 
19. Methods of applied fourier analysis [1998]
 Ramanathan, Jayakumar, 1958
 Boston : Birkhäuser, c1998.
 Description
 Book — xii, 329 p. : ill. ; 24 cm.
 Summary

 Periodic functions hardy spaces prediction theory discrete systems and control theory harmonic analysis in Euclidean space distributions functions with restricted transforms phase space wavelet analysis the discrete Fourier transform the Hermite functions.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA403.5 .R33 1998  Available 
20. Introduction to Fourier analysis [1994]
 Morrison, Norman.
 New York : Wiley, c1994.
 Description
 Book — xx, 563 p. : ill. ; 26 cm. ₊ 2 computer disks (3 1/2 in.)
 Summary

 CONTINUOUS FOURIER ANALYSIS. Background. Fourier Series for Periodic Functions. The Fourier Integral. Fourier Transforms of Some Important Functions. The Method of Successive Differentiation. FrequencyDomain Analysis. TimeDomain Analysis. The Properties. The Sampling Theorems. DISCRETE FOURIER ANALYSIS. The Discrete Fourier Transform. Inside the Fast Fourier Transform. The Discrete Fourier Transform as an Estimator. The Errors in Fast Fourier Transform Estimation. The Four Kinds of Convolution. Emulating Dirac Deltas and Differentiation on the Fast Fourier Transform. THE USER'S MANUAL FOR THE ACCOMPANYING DISKS. Appendices. Answers to the Exercises. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks

Request 
QA403.5 .M67 1994  Available 
Articles+
Journal articles, ebooks, & other eresources
 Articles+ results include